Topological Deep Learning: Going Beyond Graph Data


Over the past decade, deep learning has been remarkably successful at solving a massive set of problems on datatypes including images and sequential data. This success drove the extension of deep learning to other discrete domains such as sets, point clouds, graphs, 3D shapes, and discrete manifolds. While many of the extended schemes have successfully tackled notable challenges in each domain, the plethora of fragmented frameworks have created or resurfaced many long-standing problems in deep learning such as explainability, expressiveness and generalizability. Moreover, theoretical development proven over one discrete domain does not naturally apply to the other domains. Finally, the lack of a cohesive mathematical framework has created many ad hoc and inorganic implementations and ultimately limited the set of practitioners that can potentially benefit from deep learning technologies. This talk introduces the foundation of topological deep learning, a rapidly growing field that is concerned with the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations including images and sequence data. It introduces the main notions while maintaining intuitive conceptualization, implementation and relevance to a wide range of practical applications. It also demonstrates the practical relevance of this framework with practical applications ranging from drug discovery to mesh and image segmentation.


Dr. Hajij is an Assistant Professor specializing in data science at the University of San Francisco’s Master of Science in Data Science Program. With over 8 years of research and industrial experience, he has delved into graph neural networks, topological data analysis, intelligent transportation, and topological deep learning. His expertise extends to industrial AI applications, with a focus on topological deep learning, geometric data processing, time-varying data, and predictive modeling. He co-founded AltumX, a startup utilizing deep learning for intelligent road network systems, and actively participates in AI-related workshops and conferences. He published more than 70 publications in journal and conference papers, as well as patents. Hajij served as the main organizer for MICCAI TDA workshops in 2021 and 2022. He made contributions to the tech industry, spearheading the development of innovative software solutions for both KLA Corporation and AltumX Inc.

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